Romano, Daniel Abraham On regular anti-congruence in anti-ordered semigroups. (English) Zbl 1247.03133 Publ. Inst. Math., Nouv. Sér. 81(95), 95-102 (2007). Summary: For an anti-congruence \(q\) we say that it is a regular anti-congruence on the semigroup \((S,=, \neq, \cdot, \alpha)\) ordered under an anti-order \(\alpha\) if there exists an anti-order \(\theta\) on \(S/q\) such that the natural epimorphism is a reverse isotone homomorphism of semigroups. An anti-congruence \(q\) is regular if there exists a quasi-antiorder \(\sigma\) on \(S\) under \(\alpha\) such that \(q = \sigma\cup \sigma^{-1}\). Besides, for a regular anti-congruence \(q\) on \(S\), a construction of the maximal quasi-antiorder relation under \(\alpha\) with respect to \(q\) is shown. MSC: 03F65 Other constructive mathematics 06F05 Ordered semigroups and monoids 20M99 Semigroups Keywords:constructive mathematics; semigroup with apartness; anti-ordered semigroup; anti-congruence; regular anti-congruence; quasi-antiorder PDFBibTeX XMLCite \textit{D. A. Romano}, Publ. Inst. Math., Nouv. Sér. 81(95), 95--102 (2007; Zbl 1247.03133) Full Text: DOI